Identifying Oriented Spin Space Groups and Related Physical Properties Using an Online Platform FINDSPINGROUP

Abstract: Unconventional magnets that combine antiferromagnetic structures with ferromagnetic-like responses are essential for the development of next-generation spintronics. Their emergent properties are fundamentally dictated by the interplay between exchange-driven magnetic geometry and spin-orbit coupling, which are described by spin space group (SSG) and magnetic space group (MSG) frameworks, respectively. However, the lack of direct correspondence between these frameworks, developed in different eras, hinders the systematic tracking of symmetry evolution of these intertwined physical contributions. In this work, we introduce FINDSPINGROUP, a computational architecture that implements the recently emerged, oriented spin space group framework to unify SSG and MSG descriptions. By automating the tracking of symmetry-breaking pathways from the non-relativistic to the relativistic limit, this online platform enables the classification of magnetic phases and the derivation of symmetry-constrained tensors for phenomena such as momentum-dependent spin splitting and the anomalous Hall effect. By standardizing data exchange through the spin crystallographic information file, this architecture establishes a computational infrastructure for the high-throughput discovery and design of unconventional magnets.